// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#ifndef EIGEN_TRANSLATION_H
#define EIGEN_TRANSLATION_H

namespace Eigen {

/** \geometry_module \ingroup Geometry_Module
  *
  * \class Translation
  *
  * \brief Represents a translation transformation
  *
  * \tparam _Scalar the scalar type, i.e., the type of the coefficients.
  * \tparam _Dim the  dimension of the space, can be a compile time value or Dynamic
  *
  * \note This class is not aimed to be used to store a translation transformation,
  * but rather to make easier the constructions and updates of Transform objects.
  *
  * \sa class Scaling, class Transform
  */
template <typename _Scalar, int _Dim> class Translation
{
public:
    EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(_Scalar, _Dim)
    /** dimension of the space */
    enum
    {
        Dim = _Dim
    };
    /** the scalar type of the coefficients */
    typedef _Scalar Scalar;
    /** corresponding vector type */
    typedef Matrix<Scalar, Dim, 1> VectorType;
    /** corresponding linear transformation matrix type */
    typedef Matrix<Scalar, Dim, Dim> LinearMatrixType;
    /** corresponding affine transformation type */
    typedef Transform<Scalar, Dim, Affine> AffineTransformType;
    /** corresponding isometric transformation type */
    typedef Transform<Scalar, Dim, Isometry> IsometryTransformType;

protected:
    VectorType m_coeffs;

public:
    /** Default constructor without initialization. */
    EIGEN_DEVICE_FUNC Translation() {}
    /**  */
    EIGEN_DEVICE_FUNC inline Translation(const Scalar& sx, const Scalar& sy)
    {
        eigen_assert(Dim == 2);
        m_coeffs.x() = sx;
        m_coeffs.y() = sy;
    }
    /**  */
    EIGEN_DEVICE_FUNC inline Translation(const Scalar& sx, const Scalar& sy, const Scalar& sz)
    {
        eigen_assert(Dim == 3);
        m_coeffs.x() = sx;
        m_coeffs.y() = sy;
        m_coeffs.z() = sz;
    }
    /** Constructs and initialize the translation transformation from a vector of translation coefficients */
    EIGEN_DEVICE_FUNC explicit inline Translation(const VectorType& vector) : m_coeffs(vector) {}

    /** \brief Returns the x-translation by value. **/
    EIGEN_DEVICE_FUNC inline Scalar x() const { return m_coeffs.x(); }
    /** \brief Returns the y-translation by value. **/
    EIGEN_DEVICE_FUNC inline Scalar y() const { return m_coeffs.y(); }
    /** \brief Returns the z-translation by value. **/
    EIGEN_DEVICE_FUNC inline Scalar z() const { return m_coeffs.z(); }

    /** \brief Returns the x-translation as a reference. **/
    EIGEN_DEVICE_FUNC inline Scalar& x() { return m_coeffs.x(); }
    /** \brief Returns the y-translation as a reference. **/
    EIGEN_DEVICE_FUNC inline Scalar& y() { return m_coeffs.y(); }
    /** \brief Returns the z-translation as a reference. **/
    EIGEN_DEVICE_FUNC inline Scalar& z() { return m_coeffs.z(); }

    EIGEN_DEVICE_FUNC const VectorType& vector() const { return m_coeffs; }
    EIGEN_DEVICE_FUNC VectorType& vector() { return m_coeffs; }

    EIGEN_DEVICE_FUNC const VectorType& translation() const { return m_coeffs; }
    EIGEN_DEVICE_FUNC VectorType& translation() { return m_coeffs; }

    /** Concatenates two translation */
    EIGEN_DEVICE_FUNC inline Translation operator*(const Translation& other) const { return Translation(m_coeffs + other.m_coeffs); }

    /** Concatenates a translation and a uniform scaling */
    EIGEN_DEVICE_FUNC inline AffineTransformType operator*(const UniformScaling<Scalar>& other) const;

    /** Concatenates a translation and a linear transformation */
    template <typename OtherDerived> EIGEN_DEVICE_FUNC inline AffineTransformType operator*(const EigenBase<OtherDerived>& linear) const;

    /** Concatenates a translation and a rotation */
    template <typename Derived> EIGEN_DEVICE_FUNC inline IsometryTransformType operator*(const RotationBase<Derived, Dim>& r) const
    {
        return *this * IsometryTransformType(r);
    }

    /** \returns the concatenation of a linear transformation \a l with the translation \a t */
    // its a nightmare to define a templated friend function outside its declaration
    template <typename OtherDerived> friend EIGEN_DEVICE_FUNC inline AffineTransformType operator*(const EigenBase<OtherDerived>& linear, const Translation& t)
    {
        AffineTransformType res;
        res.matrix().setZero();
        res.linear() = linear.derived();
        res.translation() = linear.derived() * t.m_coeffs;
        res.matrix().row(Dim).setZero();
        res(Dim, Dim) = Scalar(1);
        return res;
    }

    /** Concatenates a translation and a transformation */
    template <int Mode, int Options> EIGEN_DEVICE_FUNC inline Transform<Scalar, Dim, Mode> operator*(const Transform<Scalar, Dim, Mode, Options>& t) const
    {
        Transform<Scalar, Dim, Mode> res = t;
        res.pretranslate(m_coeffs);
        return res;
    }

    /** Applies translation to vector */
    template <typename Derived>
    inline typename internal::enable_if<Derived::IsVectorAtCompileTime, VectorType>::type operator*(const MatrixBase<Derived>& vec) const
    {
        return m_coeffs + vec.derived();
    }

    /** \returns the inverse translation (opposite) */
    Translation inverse() const { return Translation(-m_coeffs); }

    static const Translation Identity() { return Translation(VectorType::Zero()); }

    /** \returns \c *this with scalar type casted to \a NewScalarType
    *
    * Note that if \a NewScalarType is equal to the current scalar type of \c *this
    * then this function smartly returns a const reference to \c *this.
    */
    template <typename NewScalarType>
    EIGEN_DEVICE_FUNC inline typename internal::cast_return_type<Translation, Translation<NewScalarType, Dim>>::type cast() const
    {
        return typename internal::cast_return_type<Translation, Translation<NewScalarType, Dim>>::type(*this);
    }

    /** Copy constructor with scalar type conversion */
    template <typename OtherScalarType> EIGEN_DEVICE_FUNC inline explicit Translation(const Translation<OtherScalarType, Dim>& other)
    {
        m_coeffs = other.vector().template cast<Scalar>();
    }

    /** \returns \c true if \c *this is approximately equal to \a other, within the precision
    * determined by \a prec.
    *
    * \sa MatrixBase::isApprox() */
    EIGEN_DEVICE_FUNC bool isApprox(const Translation& other, const typename NumTraits<Scalar>::Real& prec = NumTraits<Scalar>::dummy_precision()) const
    {
        return m_coeffs.isApprox(other.m_coeffs, prec);
    }
};

/** \addtogroup Geometry_Module */
//@{
typedef Translation<float, 2> Translation2f;
typedef Translation<double, 2> Translation2d;
typedef Translation<float, 3> Translation3f;
typedef Translation<double, 3> Translation3d;
//@}

template <typename Scalar, int Dim>
EIGEN_DEVICE_FUNC inline typename Translation<Scalar, Dim>::AffineTransformType Translation<Scalar, Dim>::operator*(const UniformScaling<Scalar>& other) const
{
    AffineTransformType res;
    res.matrix().setZero();
    res.linear().diagonal().fill(other.factor());
    res.translation() = m_coeffs;
    res(Dim, Dim) = Scalar(1);
    return res;
}

template <typename Scalar, int Dim>
template <typename OtherDerived>
EIGEN_DEVICE_FUNC inline typename Translation<Scalar, Dim>::AffineTransformType Translation<Scalar, Dim>::operator*(const EigenBase<OtherDerived>& linear) const
{
    AffineTransformType res;
    res.matrix().setZero();
    res.linear() = linear.derived();
    res.translation() = m_coeffs;
    res.matrix().row(Dim).setZero();
    res(Dim, Dim) = Scalar(1);
    return res;
}

}  // end namespace Eigen

#endif  // EIGEN_TRANSLATION_H
